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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 73920s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.by1 | 73920s1 | \([0, -1, 0, -8981, 680781]\) | \(-4890195460096/9282994875\) | \(-152092588032000\) | \([]\) | \(248832\) | \(1.4111\) | \(\Gamma_0(N)\)-optimal |
| 73920.by2 | 73920s2 | \([0, -1, 0, 77419, -14387379]\) | \(3132137615458304/7250937873795\) | \(-118799366124257280\) | \([]\) | \(746496\) | \(1.9604\) |
Rank
sage: E.rank()
The elliptic curves in class 73920s have rank \(1\).
Complex multiplication
The elliptic curves in class 73920s do not have complex multiplication.Modular form 73920.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
